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Topic: [HM] right angle
Replies: 10   Last Post: Jun 23, 2001 6:34 PM

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Alfred Ross

Posts: 56
Registered: 12/3/04
Re: [HM] Another etymological question: the word "function"
Posted: Jun 23, 2001 2:55 PM
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The word FUNCTION first appears in a Latin manuscript "Methodus
tangentium inversa, seu de fuctionibus" written by Gottfried
Wilhelm Leibniz (1646-1716) in 1673. Leibniz used the word in the
non-analytical sense, as a magnitude which performs a special duty.
He considered a function in terms of "mathematical job" -- the
"employee" being just a curve. He apparently conceived of a line
doing "something" in a given _figura_ ["aliis linearum in figura
data functiones facientium generibus assumtis"]. From the beginning
of his manuscript, however, Leibniz demonstrated that he already
possessed the idea of function, a term he denominates _relatio_.

A paper "De linea ex lineis numero infinitis ordinatim..." in the
_Acta Eruditorum_ of April 1692, pp. 169-170, signed "O. V. E." but
probably written by Leibniz, uses _functiones_ in a sense to denote
the various 'offices' which a straight line may fulfill in relation
to a curve, viz. its tangent, normal, etc.

In the _Acta Eruditorum_ of July 1694, "Nova Calculi differentialis..."
(page 316), Leibniz used the word function almost in its technical
sense, defining function as "a part of a straight line which is cut
off by straight lines drawn solely by means of a fixed point, and
of a point in the curve which is given together with its degree of
curvature." The examples given were the ordinate, abscissa, tangent,
normal, etc. [Cf. page 150 of Leibniz' "Mathematische Schriften,"
vol. III, edited by C. I. Gerhardt, Berlin-Halle (Asher-Schmidt),

In September 1694, Johann Bernoulli wrote in a letter to Leibniz,
"quantitatem quomodocunque formatam ex indeterminatis et constantibus,"
although there is no explicit reference to the Latin term _functio_.
The letter appears in "Mathematische Schriften."

On July 5, 1698, Johann Bernoulli, in another letter to Leibniz, for
the first time deliberately assigned a specialized use of the term
_function_ in the analytical sense, writing "earum [applicatarum]
quaecunque functiones per alias applicatas PZ expressae." (Cajori
1919, page 211) [Cf. page 507 of Leibniz' "Mathematische Schriften,"
vol. III, edited by C. I. Gerhardt, Berlin-Halle (Asher-Schmidt),
1849-63. Also see pages 506-510 and 525-526]. At the end of that
month, Leibniz replied (p. 526), showing his approval.

_Function_ is found in English in 1779 in Chambers' Cyclopedia: "The
term function is used in algebra, for an analytical expression any
way compounded of a variable quantity, and of numbers, or constant
quantities" (OED2).

(Information for this entry was provided by Julio Gonzalez Cabillon
and the OED2.)


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